Broad experimental design

FIGURE 11.23 Power analysis.The desired difference is >2 standard deviation units (X, - / = 8). The sample distribution in panel a is wide and only 67% of the distribution values are > 8. Therefore, with an experimental design that yields the sample distribution shown in panel a will have a power of 67% to attain the desired endpoint. In contrast, the sample distribution shown in panel b is much less broad and 97% of the area under the distribution curve is >8. Therefore, an experimental design yielding the sample distribution shown in panel B will gave a much higher power (97%) to attain the desired end point. One way to decrease the broadness of sample distributions is to increase the sample size. 

There are broadly two uses of chemometrics that interest the process chemist. The first of these is simply data display. It is a truism that the human eye is the best analytical tool, and by displaying multivariate data in a way that can be easily assimilated by eye a number of diagnostic assessments can be made of the state of health of a process, or of reasons for its failure [ 153], a process known as MSPC [154—156]. The key concept in MSPC is the acknowledgement that variability in process quality can arise not just by variation in single process parameters such as temperature, but by subtle combinations of process parameters. This source of product variability would be missed by simple control charts for the individual process parameters. This is also the concept behind the use of experimental design during process development in order to identify such variability in the minimum number of experiments. 

This chapter will examine the application of statistical experimental design to designing a product or process that is robust to variation from environmental variables. It should be understood that the phrase environmental variables is to be viewed broadly and is not just limited to variables such as temperature and humidity. In this context, variation from environmental variables is variation that is external to the product and that is outside of the control of the manufacturer during production. Thus, it might also include variation in the conditions in which the customer uses the product, or in the conditions in which the product is stored, or in how the product is maintained and serviced. 

With due deference to the myriad mathematics dissertations and journal articles on the subject of optimization, f will briefly mention some of the general approaches to finding an optimum and then describe the recommended methods of experimental design in some detail. There are two broad classes that define the options systems that are sufficiently described by a priori mathematical equations, called models, and systems that are not explicitly described, called model free. Once the parameters of a model are known, it is often quite trivial, via the miracles of differentiation, to find the maximum (maxima). 

The term parametric test, or analysis, is introduced in Section 6.2.4. In broad terms, statistical analyses can be placed into one of two categories, parametric tests and nonparametric tests. This book almost exclusively discusses parametric tests, but it should be noted here that nonparametric tests are also very valuable analyses in appropriate circumstances. As with the terms experimental design and nonexperimental design (recall Section 5.5), the term nonparametric is not a relative quality judgment compared with parametric. This nomenclature simply differentiates statistical approaches. In circumstances where nonparametric analyses are appropriate, they are powerful tests. 

The calibration samples must cover a sufficiently broad range of composition that a suitable change in measured response is instrumentally detectable. For simple systems, it is usually possible to prepare mixtures according to the principles of experimental design, where concentrations for all ingredients are varied over a suitable range. This is necessary to ensure that the measured set of mixtures has exemplars where different interactions between ingredients are present. 

These experimental designs are known as balanced incomplete blocks. They are balanced because each treatment occurs to exactly the same extent they are incomplete because no block contains the full number of treatments. They suffer from the restriction that balanced arrangements are not possible for all experimental set-ups. Broadly speaking, if we fix the number of treatments that we wish to compare, and if the number of experiments per batch (or block ) is also fixed, then the number of replication of each treatment is thereby determined. This is the principal disadvantage of these designs the number of replications they require may be greater than we think are necessary to attain sufficient accuracy. 

The levels selected in a robustness test are different from those at which factors are evaluated in method optimization. For optimization purposes the variables are examined in a broad interval. In robustness testing the levels are much less distant. They represent the (somewhat exaggerated) variations in the values of the variables that could occur when a method is transferred. For instance, in optimization the levels for pH would be several units apart, while in robustness testing the difference could be 0.2 pH units. The levels can for instance be defined based on the uncertainty with which a factor level can be set and re.set 36 and usually they are situated around the method (nominal) conditions if the method specifies pH 4.0, the levels would be 3.9 and 4.1. The experimental designs used are in both situations the same and comprise fractional factorial and Plackett-Burman designs. 

Janson and Hedman (1) recently published an excellent review of large-scale chromatography. Many of the broad process design and operation considerations are the same for affinity chromatography as they are for ion exchange or gel filtration. Most chromatography models, however, are based on the assumption of small feed pulses with linear equilibria (such as the widely-used plate theories (2)) and are not directly useful for affinity separations. In this paper we discuss and compare experimental results with two fixed-bed adsorption models that can be used to predict the performance of affinity columns. These two models differ only in the form of the rate-... 

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